Generalized thermoelastic solutions for the axisymmetric plane strain problem

Thermal disturbance propagates in the elastic medium with a finite speed during the transient heat transfer, which leads to the thermal-mechanical behavior of materials being significantly different than that of conventional heat transfer. The axisymmetric plane strain problem is investigated in this paper, the generalized thermoelastic solutions for different generalized thermoelasticity are derived by means of the Laplace transform and its limit theorem and the asymptotic formulas of Bessel functions. A case of an infinite axisymmetric medium with a cylindrical hole under thermal shock is analyzed. It is pointed out that each of physical field has a phased distribution when the propagation of thermal disturbance with a finite speed, and both the temperature and stresses have jumps at the location of thermal elastic wavefront and thermal wavefront. The L-S and G-N theories predict similar patterns for the distributions of displacement, temperature and stresses in the transient thermal shock problem, but for G-L theory a Dirac-delta-type result for the stresses is predicted and the displacement is discontinuous at both the wavefronts.